9th Grade Radicals Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the 9th Grade exponents & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheet9th Grade · Mathematics · Indices & Scientific Notation9th Grade Radicals Worksheet — Level 2 — Practice Set 4 — Answers
Write each answer in simplest radical form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √96.
Answer: 4√6
- 96 = 16 × 6
- √96 = √16 × √6 = 4√6
2.Simplify 8√13 + 3√13.
Answer: 11√13
- These are like radicals (both √13)
- 8 + 3 = 11, so 11√13
3.Simplify √52 + √208.
Answer: 6√13
- √52 = 2√13 and √208 = 4√13
- 2√13 + 4√13 = 6√13
4.Simplify √99 × √44.
Answer: 66
- √99 × √44 = √4356
- √4356 = 66
5.Simplify √40.
Answer: 2√10
- 40 = 4 × 10
- √40 = √4 × √10 = 2√10
6.Simplify 6√15 + 5√15.
Answer: 11√15
- These are like radicals (both √15)
- 6 + 5 = 11, so 11√15
7.Simplify √12 + √27.
Answer: 5√3
- √12 = 2√3 and √27 = 3√3
- 2√3 + 3√3 = 5√3
8.Simplify √5 × √7.
Answer: √35
- √5 × √7 = √35
- 35 has no square factor, so √35 is simplest
9.Simplify √640.
Answer: 8√10
- 640 = 64 × 10
- √640 = √64 × √10 = 8√10
10.Simplify 4√7 + 4√7.
Answer: 8√7
- These are like radicals (both √7)
- 4 + 4 = 8, so 8√7
11.Simplify √160 + √40.
Answer: 6√10
- √160 = 4√10 and √40 = 2√10
- 4√10 + 2√10 = 6√10
12.Simplify √3 × √7.
Answer: √21
- √3 × √7 = √21
- 21 has no square factor, so √21 is simplest
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.